SUMMARY: Identifying differentially expressed (DE) genes along cell pseudotime is crucial for understanding dynamic biological processes captured by single-cell RNA sequencing. However, existing DE methods either produce invalid P-values by ignoring the uncertainty in pseudotime inference or struggle to scale with the growing size of modern datasets. To address these limitations, we introduce PseudotimeDE-fast, a scalable method for detecting DE genes along pseudotime with well-calibrated P-values. Through comprehensive simulations and real-data analyses, we demonstrate that PseudotimeDE-fast delivers comparable or superior performance to existing approaches while offering substantial improvements in computational efficiency. AVAILABILITY AND IMPLEMENTATION: PseudotimeDE-fast is implemented in R with Rcpp acceleration and released under the MIT license. The source code is available at: https://github.com/dsong-lab/PseudotimeDE.

The Neyman-Pearson (NP) binary classification paradigm constrains the more severe type of error (e.g., the type I error) under a preferred level while minimizing the other (e.g., the type II error). This paradigm is suitable for applications such as severe disease diagnosis, fraud detection, among others. A series of NP classifiers have been developed to guarantee the type I error control with high probability. However, these existing classifiers involve a sample splitting step: a mixture of class 0 and class 1 observations to construct a scoring function and some left-out class 0 observations to construct a threshold. This splitting enables classifier threshold construction built upon independence, but it amounts to insufficient use of data for training and a potentially higher type II error. Leveraging a canonical linear discriminant analysis (LDA) model, we derive a quantitative CLT for a certain functional of quadratic forms of the inverse of sample and population covariance matrices, and based on this result, develop for the first time NP classifiers without splitting the training sample. Numerical experiments have confirmed the advantages of our new non-splitting parametric strategy.

The Neyman-Pearson (NP) paradigm in binary classification seeks classifiers that achieve a minimal type II error while enforcing the prioritized type I error controlled under some user-specified level $\alpha$. This paradigm serves naturally in applications such as severe disease diagnosis and spam detection, where people have clear priorities among the two error types. Recently, Tong, Feng, and Li (2018) proposed a nonparametric umbrella algorithm that adapts all scoring-type classification methods (e.g., logistic regression, support vector machines, random forest) to respect the given type I error (i.e., conditional probability of classifying a class $0$ observation as class $1$ under the 0-1 coding) upper bound $\alpha$ with high probability, without specific distributional assumptions on the features and the responses. Universal the umbrella algorithm is, it demands an explicit minimum sample size requirement on class $0$, which is often the more scarce class, such as in rare disease diagnosis applications. In this work, we employ the parametric linear discriminant analysis (LDA) model and propose a new parametric thresholding algorithm, which does not need the minimum sample size requirements on class $0$ observations and thus is suitable for small sample applications such as rare disease diagnosis. Leveraging both the existing nonparametric and the newly proposed parametric thresholding rules, we propose four LDA-based NP classifiers, for both low- and high-dimensional settings. On the theoretical front, we prove NP oracle inequalities for one proposed classifier, where the rate for excess type II error benefits from the explicit parametric model assumption. Furthermore, as NP classifiers involve a sample splitting step of class $0$ observations, we construct a new adaptive sample splitting scheme that can be applied universally to NP classifiers, and this adaptive strategy reduces the type II error of these classifiers. The proposed NP classifiers are implemented in the R package nproc.